# Probabilistic learning constrained by realizations using a weak formulation of Fourier transform of probability measures

@article{Soize2022ProbabilisticLC, title={Probabilistic learning constrained by realizations using a weak formulation of Fourier transform of probability measures}, author={Christian Soize}, journal={ArXiv}, year={2022}, volume={abs/2205.03078} }

This paper deals with the taking into account a given set of realizations as constraints in the Kullback-Leibler minimum principle, which is used as a probabilistic learning algorithm. This permits the effective integration of data into predictive models. We consider the probabilistic learning of a random vector that is made up of either a quantity of interest (unsupervised case) or the couple of the quantity of interest and a control parameter (supervised case). A training set of independent…

## References

SHOWING 1-10 OF 81 REFERENCES

### Entropy optimization principles with applications

- Computer Science
- 1992

Applications of Jaynes' maximum entropy principle and Kullback's minimum cross-entropy principle are applied to develop new entropy optimization principles generalized principles of maximum entropy the four inverse maximum entropy principles.

### Probabilistic learning inference of boundary value problem with uncertainties based on Kullback-Leibler divergence under implicit constraints

- Computer Science, MathematicsComputer Methods in Applied Mechanics and Engineering
- 2022

### Probabilistic learning on manifolds constrained by nonlinear partial differential equations for small datasets

- Computer Science, MathematicsComputer Methods in Applied Mechanics and Engineering
- 2021

### Physics‐constrained non‐Gaussian probabilistic learning on manifolds

- Computer Science, MathematicsInternational Journal for Numerical Methods in Engineering
- 2019

The method consists in constructing a generator using the PLoM and the classical Kullback‐Leibler minimum cross‐entropy principle and the resulting optimization problem is reformulated using Lagrange multipliers associated with the constraints.

### Nonlinear stochastic dynamics of detuned bladed-disks with uncertain mistuning and detuning optimization using a probabilistic machine learning tool

- Computer ScienceInternational Journal of Non-Linear Mechanics
- 2022

### Stochastic elliptic operators defined by non-gaussian random fields with uncertain spectrum

- Mathematics
- 2021

This paper present a construction and the analysis of a class of non-Gaussian positive-definite matrix-valued homogeneous random fields with uncertain spectral measure for stochastic elliptic…

### Probabilistic learning on manifolds (PLoM) with partition

- Mathematics, Computer ScienceInternational Journal for Numerical Methods in Engineering
- 2021

Improvements of the probabilistic learning on manifolds are presented such as a simplified algorithm for constructing the diffusion‐map basis and a new mathematical result for quantifying the concentration of the probability measure in terms of a probability upper bound.

### COMPUTATION OF SOBOL INDICES IN GLOBAL SENSITIVITY ANALYSIS FROM SMALL DATA SETS BY PROBABILISTIC LEARNING ON MANIFOLDS

- Computer ScienceInternational Journal for Uncertainty Quantification
- 2021

The objective of the probabilistic learning is to learn from the available samples a Probabilistic model that can be used to generate additional samples, from which Monte Carlo estimates of the global sensitivity indices are then deduced.

### Probabilistic learning and updating of a digital twin for composite material systems

- Computer ScienceInternational Journal for Numerical Methods in Engineering
- 2020

Conditional regression is carried out using the estimated joint density function, permitting a systematic exploration of interdependence between fine scale and coarse observables that can be used for both prognosis and design of complex material systems.

### Probabilistic learning on manifolds

- Mathematics, Computer ScienceFoundations of Data Science
- 2019

It is proven that this transported measure is a marginal distribution of the invariant measure of a reduced-order Ito stochastic differential equation that corresponds to a dissipative Hamiltonian dynamical system.